Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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T-S Fuzzy Model-Based Adaptive Synchronization of Chaotic System with Unknown Parameters

T-S 퍼지 모델을 이용한 불확실한 카오스 시스템의 적응동기화

  • 김재훈 (연세대학교 전기전자공학과) ;
  • 박창우 (전자부품연구원 정밀기기연구센터) ;
  • 김은태 (연세대학교 전기전자공학과) ;
  • 박민용 (연세대학교 전기전자공학과)
  • Published : 2005.04.01
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Abstract

This paper presents a fuzzy model-based adaptive approach for synchronization of chaotic systems which consist of the drive and response systems. Takagi-Sugeno (T-S) fuzzy model is employed to represent the chaotic drive and response systems. Since the parameters of the drive system are assumed unknown, we design the response system that estimates the parameters of the drive system by adaptive strategy. The adaptive law is derived to estimate the unknown parameters and its stability is guaranteed by Lyapunov stability theory. In addition, the controller in the response system contains two parts: one part that can stabilize the synchronization error dynamics and the other part that estimates the unknown parameters. Numerical examples, including Doffing oscillator and Lorenz attractor, are given to demonstrate the validity of the proposed adaptive synchronization approach.

본 논문은 퍼지 모델을 이용한 불확실한 카오스 시스템의 적응 동기화 기법을 제안한다. 카오스 동기화 시스템은 마스터 시스템과 슬레이브 시스템으로 구성되며 각각의 시스템은 Takagi-Sugeno (T-S) 퍼지 모델을 통해 표현된다. 마스터 시스템은 파라미터가 미리 알려지지 않은 불확실한 모델로 가정되므로 불확실한 파라미터를 추정하기 위해 적응 기법을 적용하여 슬레이브 시스템을 설계한다. 동기화 오차 시스템을 안정화하고 불확실한 파라미터를 추정하는 적응 규칙을 이용한 제어기를 설계하며 Lyapunov 이론을 통해 안정도를 해석한다. 제안된 퍼지 적응 동기화 기법의 효과를 확인하기 위해서 Duffing 시스템과 Lorenz 시스템에 대해 모의 실험을 수행한다.

Keywords

References

  1. T. L. Carroll and L. M. Pecora, 'Synchronizing chaotic circuits,' IEEE Trans. Circuits Syst. I, vol. 38, pp.453-456, 1991 https://doi.org/10.1109/31.75404
  2. K. M. Cuomo, A. V. Oppenheim, and S. H. Strogatz, 'Synchronization of Lorenz-based chaotic circuits with applications to communications,' IEEE Trans. Circuits Syst. II, vol. 40, pp. 626-633, 1993 https://doi.org/10.1109/82.246163
  3. P. Parmananda, 'Synchronization using linear and nonlinear feedbacks: a comparison,' Physics Letters A, vol. 240, pp. 55-59, 1998 https://doi.org/10.1016/S0375-9601(98)00039-5
  4. Z. Huang and J. Ruan, 'Synchronization of chaotic systems by linear feedback controller,' Communications in Nonlinear Science and Numerical Simulation, vol. 3, no. 1, pp. 27-30, 1998 https://doi.org/10.1016/S1007-5704(98)90055-7
  5. S. Chen and J. Lu, 'Parameters identification and synchronization of chaotic systems based upon adaptive control,' Physics Letters A, vol. 299, pp. 353-358, 2002 https://doi.org/10.1016/S0375-9601(02)00522-4
  6. Y. Wang, Z. Guan, and X. Wen, 'Adaptive synchronization for Chen chaotic system with fully unknown parameters,' Chaos, Solitons and Fractals, vol. 19, pp. 899-903, 2004 https://doi.org/10.1016/S0960-0779(03)00256-X
  7. E. M. Elabbasy, H. N. Agiza, and M. M. El-Dessoky, 'Adaptive synchronization of Lu system with uncertain parameters,' Chaos, Solitons and Fractals, vol. 21, pp. 657-667, 2004 https://doi.org/10.1016/j.chaos.2003.12.028
  8. K. Tanaka and M. Sugeno, 'Stability analysis and design of fuzzy control systems', Fuzzy Sets and Syst., vol. 45, no. 2, pp. 135-156, 1992 https://doi.org/10.1016/0165-0114(92)90113-I
  9. T. Takagi and M. Sugeno, 'Fuzzy identification of systems and its applications to modeling and control,' IEEE Trans. Syst., Man, Cybern., vol. 15, pp. 116-132, 1985
  10. K. Tanaka, T. Ikeda, and H. O. Wang, 'A unified approach to controling chaos via an LMI-based fuzzy control system design,' IEEE Trans. Circuits Syst. I, vol. 45, pp. 1021-1040, 1998 https://doi.org/10.1109/81.728857
  11. K. -Y. Lian, C. -S. Chiu, T. -S. Chiang, and P. Liu, 'LMI-based fuzzy chaotic synchronization and communications,' IEEE Tans. Fuzzy Syst., vol. 9, no. 4, pp. 539-553, 2001 https://doi.org/10.1109/91.940967
  12. K. -Y. Lian, T. -S. Chiang, C. -S. Chiu, and P. Liu, 'Synthesis of fuzzy model-based designs to synchronization and secure communications for chaotic systems,' IEEE Trans. Syst., Man, Cybern. B, vol. 31, pp. 66-83, 2001 https://doi.org/10.1109/3477.907565
  13. S. H. Strogatz, Nonlinear Dynamics and Chaos, Westview Press, 2001